Game Development Reference
Complete the table by performing the inversion calculation process for the flows leav-
ing each state on the TFD. Go from state to state and fill in the table as you go along.
Start at the top of the diagram with the NoPointsItemLocked state. Do inversion calcula-
tion for flows 3 and 14. Since these flows have the identical value of 50%, there's no
need to do any math. The inverted result in this case is the same as the original. Put
50's in the table for these flows, as shown in Figure 12.23.
Figure 12.22 Inverted flow usage table
initialized with Enter and
Exit flow data.
Figure 12.23 Fixed usage added
for flows leaving
Moving clockwise around the diagram, do the inversion for flows 2 and 4 coming
from HavePointsItemUnlocked . There are only two values, so you can swap values without
having to do a calculation. Figure 12.24 shows the 90% inverted usage for flow 2 and
the 10% inverted usage for flow 4 added to the table.
The next state on your trip around the TFD is HavePointsItemUnlocked . This is the state
that has the Exit flow, which is already recorded as 10% in the inverted table. The trick
here is to invert the other flows from this state while preserving the total usage of
100% when they are all added up, including the Exit flow. Have you figured out how
to do this? For step 1, only calculate the reciprocals of flows 5 (5%), 7 (75%), and 12
(10%). These would be 20, 1.33, and 10, respectively. The sum of the reciprocals (step
2) is 31.33. Divide each reciprocal with the sum (step 3) to get 0.638, 0.042, and 0.319.
Since it has already been established that flow 6 (Exit) accounts for 10% of the usage
probability total for HavePointsItemUnlocked , then these other three flows must account